A walk through quaternionic structures
- Degree Grantor:
- University of California, Santa Barbara. Mathematics
- Degree Supervisor:
- William B. Jacob
- Place of Publication:
- [Santa Barbara, Calif.]
- Publisher:
- University of California, Santa Barbara
- Creation Date:
- 2016
- Issued Date:
- 2016
- Topics:
- Mathematics
- Keywords:
- Abstract Witt Ring,
Combinatorics,
Graph Theory,
Quaternionic Structure,
Steiner Triple System, and
Witt Ring - Genres:
- Online resources and Dissertations, Academic
- Dissertation:
- M.A.--University of California, Santa Barbara, 2016
- Description:
In 1980, Murray Marshall proved that the category of Quaternionic Structures is naturally equivalent to the category of abstract Witt rings. This paper develops a combinatorial theory for finite Quaternionic Structures in the case where 1 = --1, by demonstrating an equivalence between finite quaternionic structures and Steiner Triple Systems (STSs) with suitable block colorings. Associated to these STSs are Block Intersection Graphs (BIGs) with induced vertex colorings. This equivalence allows for a classification of BIGs corresponding to the basic indecomposable Witt rings via their associated quaternionic structures. Further, this paper classifies the BIGs associated to the Witt rings of so-called elementary type, by providing necessary and sufficient conditions for a BIG associated to a product or group extension.
- Physical Description:
- 1 online resource (66 pages)
- Format:
- Text
- Collection(s):
- UCSB electronic theses and dissertations
- Other Versions:
- http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqm&rft_dat=xri:pqdiss:10192389
- ARK:
- ark:/48907/f3zs2wnf
- ISBN:
- 9781369340457
- Catalog System Number:
- 990047189500203776
- Copyright:
- Justin Kelz, 2016
- Rights:
- In Copyright
- Copyright Holder:
- Justin Kelz
File | Description |
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Access: Public access | |
Kelz_ucsb_0035N_13146.pdf | pdf (Portable Document Format) |